Fig. 4: Single-mode contributions to tunnelling of the magnetisation.
From: Vibronic effects on the quantum tunnelling of magnetisation in Kramers single-molecule magnets
a, c Single-mode vibronic spin-flip probabilities plotted for each vibrational mode, shown as a function of the mode axiality ΔAj = Aj−Ael relative to the electronic axiality Ael. The magnitude of the internal field is fixed to Bint = 1 mT and the external field sweep rate is 10 Oe/s. The probabilities \(\left\langle {P}_{j}\right\rangle\) are obtained by averaging over random orientations of external and internal fields. The colour coding represents the spin–phonon coupling strength \(\parallel {\hat{V}}_{j}\parallel\). Grey dashed lines corresponds to a purely electronic model. a and c correspond to amorphous \({[{{{{{{{\rm{Dy}}}}}}}}{({{{{{{{{\rm{Cp}}}}}}}}}^{{{{{{{{\rm{ttt}}}}}}}}})}_{2}]}^{+}\) and crystalline [Dy(bbpen)Br]. b, d Visual representation of the displacements induced by the vibrational modes indicated by arrows in a and c denoted by A–D; the corresponding vibrational frequencies are denoted by ωA,ωB,ωC,ωD.
